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Both the inequalities are true when we substitute x = -1 and y = 0, so (-1, 0) satisfies the system of inequalities.

An inequality expresses a relationship between two values, indicating whether one is greater than, less than, or greater than or equal to or less than or equal to the other.

To check whether the point (-1, 0) is a solution of the system of inequalities:

-7x + 3y > -1

5x - 9y > -6

We need to substitute x = -1 and y = 0 into both inequalities and check whether the resulting expressions are true or false:

-7(-1) + 3(0) > -1

==> 7 > -1 (true)

5(-1) - 9(0) > -6

==> -5 > -6 (true)

Both the inequalities are true when we substitute x = -1 and y = 0, so (-1, 0) satisfies the system of inequalities. Therefore, the answer is: option A) Yes.

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Answer:

[tex]\frac{9}{7}[/tex]

Step-by-step explanation:

[tex]\frac{6}{7}[/tex] ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{6}{7}[/tex] · [tex]\frac{3}{2}[/tex] = [tex]\frac{18}{14}[/tex] = [tex]\frac{9}{7}[/tex]

So, the answer is  [tex]\frac{9}{7}[/tex]

Answer: The area of Ryan's chessboard is given as 64x^6y^8 square units.

We know that the area of a square is given by A = s^2, where A is the area and s is the side length.

To find the side length of the square, we can use the formula for the side length of a square in terms of its area, which is s = √A.

Substituting A = 64x^6y^8, we get:

s = √(64x^6y^8)

Using the properties of square roots, we can simplify this expression as follows:

s = √(2^6 * (x^2)^3 * (y^2)^4)

s = √(2^6) * √((x^2)^3) * √((y^2)^4)

s = 2^3 * x^3 * y^4

Therefore, the expression for the side length of Ryan's chessboard is 2^3 * x^3 * y^4.

Step-by-step explanation:

Answer:

[tex]m = \frac{10 - 3}{6 - 2} = \frac{7}{4} [/tex]

Answer:

7/4.

Step-by-step explanation:

Slope = rise / run

= (10-3)/(6-2)

= 7/4.

Answer:

80π square feet

Step-by-step explanation:

Answer: You can buy a maximum of 15 gallons of gas for $54.

To see why, you can divide the total amount of money you have by the cost per gallon:

$54 ÷ $3.60/gallon = 15 gallons

Step-by-step explanation:

Answer: a) The probability of matching the first five selected numbers to the later five numbers drawn is given by the formula:

P = (C(69,5) / C(69,5)) * (C(5,5) / C(26,1))

where C(n,r) is the number of combinations of n items taken r at a time. The first term in the product represents the number of ways to choose the first five numbers from the pool of 69, and the second term represents the probability of choosing the correct number from the second set of 26 numbers.

Simplifying the expression, we get:

P = (1) * (1/26) = 1/26

Therefore, the probability of matching the first five selected numbers to the later five numbers drawn is 1/26.

b) The probability of matching the sixth selected number to the later number drawn from the second set is given by:

P = C(1,1) / C(26,1) = 1/26

Therefore, the probability of matching the sixth selected number to the later number drawn is 1/26.

c) The probability of winning the jackpot is the product of the probabilities of matching the first five selected numbers to the later five numbers drawn and matching the sixth selected number to the later number drawn. Using the results from parts (a) and (b), we get:

P = (1/26) * (1/26) = 1/676

Therefore, the probability of winning the jackpot is 1 in 676.

Step-by-step explanation:

The measure of BC is 110°

Semicircle is defined as a half circle formed by cutting the circle into two halves. It is formed when a line passes through the center and touches the two ends of the circle. This line is called the diameter of the circle.

line AB is the diameter of the circle and thus, AB gives a semi circle.

This means that, since angle Ina semi circle is 180°, the sum of AC and BC is 180°

therefore, 2x-30+x = 180°

3x = 180+30

3x = 210

divide both sides by 3

x = 210/3 = 70°

therefore BC = 2x-30

= 2×70-30

= 140-30

= 110

therefore the measure of BC is 110°

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{3}\\ o=\stackrel{opposite}{4} \end{cases} \\\\\\ x=\sqrt{ 3^2 + 4^2}\implies x=\sqrt{ 9 + 16 } \implies x=\sqrt{ 25 }\implies x=5[/tex]

The unit rate for points per game is determined by dividing the total points scored by the number of games played. In this case, 62 points  3 games = 20.67 points per game (rounded to two decimal places).

To determine the unit rate for points per game, we need to divide the total number of points scored by the number of games played. In this case, Pedro scored 62 points over the last 3 basketball games.

The unit rate for points per game is found by dividing the total points scored by the number of games played. In this case, Pedro scored 62 points over 3 basketball games, so the unit rate for points per game is:

62 points ÷ 3 games = 20.67 points per game (rounded to two decimal places)

So, none of the given options is correct. The correct answer is 62 over 3 points per game, which is equivalent to 20.67 points per game when rounded to two decimal places.

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Answer:

62.01 i took the test

Step-by-step explanation:

Option C is correct. probability of choosing man and non drinker is given s 0.932

Probability is a branch of mathematics that deals with the study of random events or experiments, and the likelihood or chance of certain outcomes occurring. It is concerned with quantifying the uncertainty of events and helps us make predictions or informed decisions in situations where the outcome is not certain.

probability of choosing man and non drinker= 209 / 425 + 322 / 425 - 135 / 425

= 0.4917 +0.7576 - 0.3176

= 0.9317

this is approximately 0.932

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Answer:

No, (-2, 3) is not a solution

Step-by-step explanation:

Substitute x with -2 and y with -3.

x = -2

-2 = -2   true

2x + 3y = 6

2(-2) + 3(3) = 6

-4 + 9 = 6

5 = 6    false

Answer:

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

We know that V = 5,890.625 cm^3, h = 14.5 cm, and l = 25 cm.

Substituting these values into the formula, we get:

5,890.625 = 25w(14.5)

5,890.625 = 362.5w

w = 16.25

Therefore, the width of the rectangular prism is 16.25 cm.

Answer:

It's A

Step-by-step explanation:
well all you have to do is divide like 5,890.625 dvided by 14.5 then divide again by 25 them bam you got 16.25

The total number of copies sold to date is approximately 369,767.

An equation can be described mathematically as a statement that supports the equality of two expressions joined by the equals sign "=". For instance, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. "=" is the sign that connects these two expressions.

Let's assume the total number of copies sold to date as x.

We know that the number of copies sold in the first month is 31,800, which is 8.6% of the total number of copies sold to date.

So we can set up an equation as follows:

31,800 = 0.086x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.086:

x = 31,800 / 0.086

x = 369,767.44

Therefore, the total number of copies sold to date is approximately 369,767.

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Answer:

600/7% OR 85.71%

Step-by-step explanation:

increase in speed =v-u

I=115-85

I=30km/h

percentage increase =(I/u) ×100

30/85 ×100

6/17×100

600/7%

The statements provided about fractions and percentage of yogurt cups and the strawberry flavor are, respectively, true, false, true, false.

In a case of 30 yogurt cups, 6 out of every 10 are strawberry. Therefore, there are a total of 18 strawberry yogurt cups in the case.

To find the fraction of yogurt cups that are strawberry, you divide the total number of strawberries (18) by the total number of cups (30), which gives 18/30.

The total number of strawberry yogurt cups is 18, based on the fact that there are 30 yogurt cups in the case.

60% of the yogurt cups are strawberry, which is the result of multiplying the fraction of strawberry yogurt cups (18/30) by 100%.

To find the percentage of yogurt cups that are not strawberry, you subtract the percentage of strawberry yogurt cups (60%) from 100%, which gives 40%.

Therefore, we can conclude we have correctly answered this question.

The complete question is the following:

Mrs. Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry. There are 30 yogurt cups in the case. Choose True or False for each statement.

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The 95% confidence interval for the average interval of violations per lawbreaker is (11.12, 18.88) and other solutions are below

a) To estimate the average interval of violations per lawbreaker, we need to calculate the sample mean and standard deviation of the 15 offenders.

Mean = (15+20+10+25+5+22+8+12+18+7+23+6+24+19+11)/15 = 15

Sample standard deviation, s = 7.01

To calculate the 95% confidence interval, we can use the formula:

CI = x ± t(α/2, n-1)*(s/√(n))

where, α= 1 - confidence level = 0.05 (for 95% confidence level)

t(a/2, n-1) = t(0.025, 14) = 2.145 (from t-table)

CI = 15 ± 2.145*(7.01/√(15))

CI = 15 ± 3.88

CI = (11.12, 18.88)

Therefore, the 95% confidence interval for the average interval of violations per lawbreaker is (11.12, 18.88)

b) To make the interval estimate of the proportion of offenders who violate the law exceed 20 times, we need to calculate the sample proportion and standard error.

Sample proportion,

p = number of offenders who violate the law more than 20 times / sample size

p = 4/15

Sample standard error,

SE = √(p*(1-p)/n)

SE = √(4/15 * 11/15 / 15) = 0.114

To calculate the 90% confidence interval, we can use the formula:

CI = p ± z(a/2)*SE

where, a= 1 - confidence level = 0.1 (for 90% confidence level)

z(a/2) = z(0.05) = 1.645 (from z-table)

CI = 4/15 ± 1.645*0.114

CI = (0.079, 0.455)

Therefore, the 90% confidence interval for the proportion of offenders who violate the law more than 20 times is (0.079, 0.455)

Using a graphing tool, we have

y = 0.89x - 0.69

r^2 = 0.9964

We can use the t-test.

The formula for the t-test is:

t = r*√(n-2) / √(1-r^2)

Also, we have

r^2 = 1 - (SSres/SStot)

Since r^2 = 0.9964, we can estimate

SSres/SStot = 0.0036

SStot = SSres/0.0036

Using these values, we can calculate the t-statistic:

t = r*√(n-2) / √(1-r^2)

t = 0.9964*√(6-2) / √(1-0.9964^2)

t = 23.51

Using a two-tailed test and a significance level of 0.05, the critical t-value with 4 degrees of freedom is ±2.101.

Since the calculated t-value (23.51) is greater than the critical t-value (2.101), we reject the null hypothesis and conclude that there is a significant correlation between the percentage increase in the number of lawyers and the percentage increase in revenue from the attorney's office.

Therefore, it is possible to predict Y using the equation y = 0.89x - 0.69. The equation is in the form of y = a + bx, where a is the y-intercept (-0.69) and b is the slope (0.89).

The equation tells us that for every 1% increase in the number of lawyers, there will be a predicted 0.89% increase in revenue from the attorney's office.

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The value of the set for the given value of set complement is n(X ∩ Y) = 92.

In set theory, a set's complement The set of all U elements that are not in A is known as A. In other words, all the components that are in U but not in A are in A'. A' is the set of odd numbers, for instance, if U is the set of integers and A is the set of even integers. In many mathematical and computational applications, the complement of a set is a crucial idea in set theory.

Given that, n(U) = 100, n(X) = 51, n(Y) = 63 and n(XUY)' = 8.

Using the formula of union of two sets we have:

n(XUY)' = n(U) - n(X ∩ Y)

Substituting the values we have:

8 = 100 - n(X ∩ Y)

n(X ∩ Y) = 100 - 8

n(X ∩ Y) = 92

Hence, the value of the set for the given value of set complement is n(X ∩ Y) = 92.

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Answer: 3.2 or 16/5

Step-by-step explanation:

the mixed number would be 3 1/5

(a)   g(x) = 2f(x) + 3.

b.)

the inverse functions are:

f-1(x) = x/2

g¹(x) = (x - 3)/2

c.)

g¹(x) = 2*f-1(x+3).

d. ) we obtain the graph of g¹(x) = 2f-1(x+3). and  g(x) = 2f(x) + 3.

(b) The inverse function of f(x) = 2*x is f-1(x) = x/2.

We found the  inverse function of g(x) = 2f(x) + 3 = 2(x) + 3, by isolating f(x):

g(x) = 2*f(x) + 3

(g(x) - 3)/2 = f(x)

f-1(x) = (x - 3)/2

(d)   we work on this graph f-1(x) and g¹(x),  by graphing f(x) = 2x and y = x/2 on the same set of axes.

shift the graph of f(x) to the right by 3 units to obtain the graph of f-1(x+3), and stretch it vertically by a factor of 2 to obtain the graph of g¹(x) = 2f-1(x+3).

The resulting graph should have a horizontal asymptote at y = 3 and pass through the points (0, -1.5) and (6, 4.5).

To produce g(x) from f(x), we will use  a vertical stretch by a factor of 2, which results in 2f(x). Then, we shift the graph 3 units upward, which results in g(x) = 2f(x) + 3.

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Answer: For each hour spent driving, the distance increases by 59.3

miles.

Step-by-step explanation:

Your welcome!

Answer:

C)  For each hour spent driving, the distance increases by 59.3 miles.

Step-by-step explanation:

In the function f(x) = 59.3x + 58.3, the coefficient of x is 59.3.

This coefficient represents the rate of change or slope of the linear relationship between distance traveled (in miles) and time (in hours).

Specifically, it represents the speed of the car in miles per hour (mph).

This means that for each hour spent driving (each unit increase in time), the car travels an additional 59.3 miles, so its distance increases by 59.3 miles each hour. Hence, the car is traveling at a speed of 59.3 mph.

The vertex of the graph of this equation y = x² - x - 2 is equal to -2.25.

In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

For the given quadratic function y = x² - x - 2 in question 9, the axis of symmetry can be calculated as follows:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-1)/2(1)

Axis of symmetry, Xmax = 1/2

Axis of symmetry, Xmax = 1/2.

Next, we would determine the vertex when x = 1/2 as follows;

y = x² - x - 2

y = (1/2)² - 1/2 - 2

y = 1/4 - 1/2 - 2

y = 0.25 - 0.5 - 2

y = -2.25.

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a) The sum of the measures of the interior angles of the regular nonagon is given by S₉ = 1260°

b) The measure of each interior angle of the regular nonagon is a = 140°

c) The measure of each exterior angle of the regular nonagon​ is b = 40°

Given data ,

Sum of the measures of the interior angles of a regular nonagon:

The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) * 180°

For a nonagon, which has 9 sides, we can plug in n = 9 into the formula:

Sum of interior angles = (9 - 2) * 180

Sum of interior angles = 7 * 180

Sum of interior angles = 1260°

So, the sum of the measures of the interior angles of a regular nonagon is 1260°

Measure of each interior angle of a regular nonagon:

Since a regular nonagon has 9 sides, we can divide the sum of the interior angles (which we calculated as 1260 degrees) by the number of sides to find the measure of each interior angle:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 1260 / 9

Measure of each interior angle = 140°

So, the measure of each interior angle of a regular nonagon is 140°

Measure of each exterior angle of a regular nonagon:

The Polygon Exterior Angle Sum Theorem states that the sum of the measures of the exterior angles of a polygon with n sides is always 360°

Since a regular nonagon has 9 sides, we can divide 360 degrees by the number of sides to find the measure of each exterior angle:

Measure of each exterior angle = 360 / Number of sides

Measure of each exterior angle = 360 / 9

Measure of each exterior angle = 40°

Hence , the measure of each exterior angle of a regular nonagon is 40°

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Answer:

3 days

Step-by-step explanation:

set up an equation 40+28x=124

solve for x

Answer: D

Step-by-step explanation:

The given expression is 2w3 + 7w2 - 4w.

The power of the expression is the highest exponent of the variable w, which is 3. However, this is not one of the options given.

A factor of the expression is a term or expression that divides the given expression completely. -4w is not a factor of the given expression.

The coefficient of a term is the numerical factor that is multiplied by the variable. The coefficient of the first term 2w3 is 2, and the coefficient of the second term 7w2 is 7. The coefficient of the last term -4w is -4. Therefore, the statement "The coefficient of the expression is w" is false.

The given expression has three terms: 2w3, 7w2, and -4w. Therefore, the statement "The expression has 3 terms" is true.

x=2,-13

Hope this helps

Mary's estimate of the population proportion would be more precise than Diego's.

Part A: The sample proportion (p) for Diego's data can be found by dividing the number of students who watch television shows on a computer (65) by the total number of students in the sample (100).

p = 65/100 = 0.65

Part B: To determine if the sample is large enough to calculate a confidence interval, we can use the rule of thumb that both np and n(1-p) should be greater than or equal to 10.

np = 100 * 0.65 = 65

n(1-p) = 100 * (1 - 0.65) = 100 * 0.35 = 35

Since both values are greater than or equal to 10, Diego's sample is large enough to calculate a confidence interval for the population proportion.

Part C: The standard error (SE) can be found using the formula:

SE = sqrt[p(1-p)/n]

SE = sqrt[0.65(1-0.65)/100]

SE = sqrt[0.65 * 0.35 / 100]

SE = sqrt[0.2275/100]

SE = sqrt[0.002275]

SE ≈ 0.048 (rounded to the nearest hundredth)

Part D: Using the empirical rule (68-95-99.7 rule), we can calculate the confidence intervals for Diego's sample proportion:

68% confidence interval = p ± 1 * SE = 0.65 ± 1 * 0.048 = (0.65 - 0.048, 0.65 + 0.048) = (0.602, 0.698)

95% confidence interval = p ± 2 * SE = 0.65 ± 2 * 0.048 = (0.65 - 0.096, 0.65 + 0.096) = (0.554, 0.746)

99.7% confidence interval = p ± 3 * SE = 0.65 ± 3 * 0.048 = (0.65 - 0.144, 0.65 + 0.144) = (0.506, 0.794)

Part E: Since Mary took a larger sample (200 students) compared to Diego (100 students), we would expect her 95% confidence interval to be narrower than Diego's. A larger sample size usually leads to a smaller standard error, which in turn results in a narrower confidence interval.

This means that Mary's estimate of the population proportion would be more precise than Diego's.

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Answer: The Tacos

Step-by-step explanation: This is because independent variable is the cause not the effect but i might be wrong because i don't have the answer options